Starting at its rightmost position, it takes 2 seconds for the pendulum of a grandfather clock to swing a horizontal distance of 18 inches from right to left and 2 seconds for the pendulum to swing back from left to right. Which of the following equations models \( d \), the horizontal distance in inches of the pendulum from the center as a function of time, \( t \), in seconds? Assume that right of center is a positive distance and left of center is a negative distance. \( d=9 \cos \left(\frac{\pi}{4} t\right) \) \( d=9 \cos \left(\frac{\pi}{2} t\right) \) \( d=18 \cos \left(\frac{\pi}{4} t\right) \) \( d=18 \cos \left(\frac{\pi}{2} t\right) \)

IV. Determinar la amplitud \( y \) el periodo de las siguientes funciones \( \begin{array}{ll}\text { 1. } y=2 \operatorname{sen} 3 x & \text { 5. } y=-\cos 2 x \\ \text { 2. } y=2 \cos 4 x & \text { 6. } y=\operatorname{sen}(-x) \\ \text { 3. } y=1+2 \cos 3 x & \text { 7. } y=1-2 \operatorname{sen} 3 x \\ \text { 4. } y=4 \tan \frac{1}{2} x & \text { 8. } y=3-\operatorname{sen} \frac{x}{2}\end{array} \)

5) \( 2 \operatorname{tg}^{2} \frac{\pi}{3}-\operatorname{ctg}^{2} \frac{\pi}{6}-\sin \frac{\pi}{6} \cdot \cos \frac{\pi}{3} \)

3) \( \sin \frac{3 \pi}{2}+\cos \frac{\pi}{2}+\sin ^{2} \frac{\pi}{4} \)

\( \begin{array}{ll}\text { 1. } y=2 \operatorname{sen} 3 x & \text { 5. } y=-\cos 2 x \\ \text { 2. } y=2 \cos 4 x & \text { 6. } y=\operatorname{sen}(-x) \\ \text { 3. } y=1+2 \cos 3 x & \text { 7. } y=1-2 \operatorname{sen} 3 x \\ \text { 4. } y=4 \tan \frac{1}{2} x & \text { 8. } y=3-\operatorname{sen} \frac{x}{2} \\ & \end{array} \)

Verify each identity. 1) \( \frac{\tan x+1}{\sec x}=\sin x+\cos x \)